A read-only transaction (ROT) or a query is a transaction that only reads data items, without modifying them. When we use a protocol that takes care of ROTs distinctively from update transactions, the number of conflicts between ROTs and update transactions can be reduced. As a result, a database system can schedule many more transactions within a given deadline, and it improves the degree of concurrency by reducing the number of data conflicts. In this paper, we propose a new concurrency control protocol for ROTs, called ROT-FREEZE, in real-time secure database systems. ROT-FREEZE improves on the freezing method that has been suggested by C. Park et al. (2000) to resolve conflicts between real-time requirements and security requirements. In ROT-FREEZE, ROTs are never aborted due to update transactions. By our performance evaluations, ROT-FREEZE is proved to be better than other legacy protocols for real-time secure database systems. We also prove that the proposed protocol guarantees serializability and satisfies both real-time and security requirements.